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Asymptotics of the Moment Generating Function for the Range of Random Walks

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  • Yuji Hamana

    (Kyushu University)

Abstract

The range of random walks means the number of distinct sites visited at least once by the random walk before time n. We are interested in the free energy function of the range of simple symmetric random walks and determine the asymptotic behavior near the origin.

Suggested Citation

  • Yuji Hamana, 2001. "Asymptotics of the Moment Generating Function for the Range of Random Walks," Journal of Theoretical Probability, Springer, vol. 14(1), pages 189-197, January.
    • Handle: RePEc:spr:jotpro:v:14:y:2001:i:1:d:10.1023_a:1007829300654
    DOI: 10.1023/A:1007829300654
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    References listed on IDEAS

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    1. Hamana, Yuji, 1998. "An almost sure invariance principle for the range of random walks," Stochastic Processes and their Applications, Elsevier, vol. 78(2), pages 131-143, November.
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    Cited by:

    1. Kazuki Okamura, 2021. "Some Results for Range of Random Walk on Graph with Spectral Dimension Two," Journal of Theoretical Probability, Springer, vol. 34(3), pages 1653-1688, September.

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